I took the liberty of reading your other two posts, about planning to buy a trawler to take from the Great Lakes down to FLA and the ICW.
An inverter (1500-2000 Watts) is a great idea. Some would say a must-have.
Assuming you don't have a proper 12VDC marine fridge, you can easily run a household (120VAC) fridge off an inverter like that. A lot of people nowadays seem to be using small (and inexpensive) household fridges in their boats, instead of expensive marine units. Not as efficient, but the cost savings is a consideration.
With an inverter, you can also run chargers for laptops, tablets and cell phones, maybe some lights if you have 120VAC fixtures, at the same time. We use the microwave (small 900W model) and a small vacuum cleaner frequently. You can plug in Christmas lights if you want to join a boat parade. You'll find lots of uses for an inverter.
Here's the important part: Whether your fridge is 12VDC or 120VAC, whether you have an inverter or not, you need to have some way to supply power when you're not underway or attached to shore power. That would be your "house" battery. Typically, this is a bank of two or more deep-cycle 6V or 12V batteries.
The house bank is rated for a given number of Amp-Hours. So if you use 100 AHs in an average 24-hour period, you need (1) a house bank of at least 200AH (since you should avoid draining it more than half-way) and (2) some way to put 100 AHs back into it at least once or twice a day.
If you have an 80A alternator on your engine, you might assume 50A available to charge the batteries at cruising speed. Thus, a minimum of two hours underway will theoretically recharge. But of course, the batteries won't accept the full 50A as they get closer to fully charged. On the other hand, it's OK to get them to 80% or 90%.
Or, if you have one, run your generator for an hour or so, twice a day, to charge batteries, heat water, cook meals, wash dishes, etc. Typical inverters used in trawlers are also battery chargers. So the batteries will be topped off during these times.
Unfortunately, you'll need to do some math to figure out your maximum AC and DC loads, your average AH usage, and what size house bank, alternator, inverter, charger, solar panels, and/or generator you'll want.
And, of course, you'll need to estimate how long you plan to be away from shore power and how long you'll be running the main engine(s) each day, on average.
There are as many different solutions to these equations as there are boaters. I'd say the numbers I used as examples above are not out of the ballpark for a lot of modest-sized cruisers, but there are many members here who find totally different values work for them.